Suppose that X1,...,X5 is a random sample from the uniform distribution with parameter θ (i.e., these are independent uniform random variables with parameter θ, where θ is unknown). Define the following estimator (a random variable that is a function of X1,...,X5): Xmax = k max(X1,...,X5), where k will be selected later. (a) Find the density of Xmax (it will depend on θ and k). (b) Find k such that Xmax is an unbiased estimator for θ.

Suppose that X1,...,X5 is a random sample from the uniform distribution with parameter θ (i.e., these are independent uniform random variables with parameter θ, where θ is unknown). Define the following estimator (a random variable that is a function of X1,...,X5): Xmax = k max(X1,...,X5), where k will be selected later. (a) Find the density of Xmax (it will depend on θ and k). (b) Find k such that Xmax is an unbiased estimator for θ.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

Suppose that X1,...,X5 is a random sample from the uniform distribution with parameter θ (i.e., these are independent uniform random variables with parameter θ, where
θ is unknown). Define the following estimator (a random variable that is a function of X1,...,X5): Xmax = k max(X1,...,X5), where k will be selected later.

(a) Find the density of Xmax (it will depend on θ and k).
(b) Find k such that Xmax is an unbiased estimator for θ.

Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.

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